On the Well-Posedness of Pocklington's Equation for a Straight Wire Antenna and Convergence of Numerical Solutions

Abstract

In this paper we describe some recent mathematical results concerning Pocklington's integro-differential equation for the current induced on a straight, thin wire by an incident harmonic electromagnetic field. These results show that this equation is well-posed in suitable function spaces and describe the continuity and smoothness properties of the solution compared with the incident field. We also describe some new rigorous convergence results for a simple Galerkin type numerical solution method for the equation.